L.A. somehow managed to get 10 games into the season without a goal from any of its centers, notably stars Kopitar and Richards, yet went 6-4-0. Kopitar and Richards emerged from their slumps Thursday night to save the Kings from a meltdown in a 7-4 win against the Phoenix Coyotes.

Kopitar got his first goal in 27 games and made a pretty no-look assist to highlight a four-goal first period that chased goalie Mike Smith. Richards scored the game-winner shorthanded and Dwight King capped his first career hat trick with an empty-net goal as the Kings snapped the Coyotes' 5-0-2 unbeaten streak in regulation.

The lack of scoring down the middle was a big storyline that Kopitar jokingly defused afterward.

"Well, [Jeff] Carter was playing center, so we had four [goals] off the bat tonight," Kopitar said.

Phoenix erased a 4-0 deficit with two goals in a 3:55 span of the second period and two more in 59 seconds early in the third before Richards took the puck from Radim Vrbata and slid a backhander past Thomas Greiss at 4:19 for his 28th career shorthanded goal, tied with Martin St. Louis of the Tampa Bay Lightning for most among active players.

Coach Darryl Sutter has been OK with the zeroes next to Kopitar's and Richards' goal totals because of their solid end-to-end games -- but he acknowledged it was good to see both score.

"You don't want to have to come from behind, and you don't want to have to score the winning goal after a four-goal lead," Sutter said. "But it was really good to see Kopi get his first and Mike get his first and [Matt] Frattin get rewarded and see [King] get rewarded.

"There's a lot of nights where those guys both do a lot of stuff where it doesn't matter about goals."

Sutter mixed up his lines, breaking up Kopitar and captain Dustin Brown. That his team scored seven goals in the first game since he juggled the lines allowed Sutter to crack wise.

"Good thing they didn't kick a field goal on the last play of the game," Sutter said.

Coyotes captain Shane Doan, a game-time decision because of a lower-body injury, tied it at 2:50 when he threw the puck on net and watched it skid through traffic and into the net to stun the Staples Center crowd.

The Coyotes' seven-game points streak effectively ended when Frattin got his first goal with the Kings at 12:11 of the third to make it 6-4. King hit the empty net with 22 seconds left.

The roller-coaster game didn't sit well with Doan.

"It looks like our season, where we can be so good at times and then we can be so bad at times," Doan said. "As leaders, we've got to talk and we've got to stick to what's fundamentally working for us because that's really what our games is: Keeping it simple and doing things right, the way that we know to, instead of trying to get off our own page."

Phoenix defenseman Rostislav Klesla left the game with a lower-body injury in the first period. Coyotes coach Dave Tippett did not have an update on Klesla.

As far as Richards' goal, Tippett was less than pleased.

"Poor execution," he said. "You get a couple of breaks to get yourself back in the game, and then give one away like that. It's not the way we want to be."

The Kings' forecheck and breakouts in the first period were reminiscent of L.A.'s 2012 Western Conference Finals win against Phoenix. They outshot the Coyotes 15-5 and scored four goals against a Phoenix team that had allowed a total of nine first-period goals through 10 games.

Kopitar grabbed a loose puck and wristed it past Smith 42 seconds into the game after Antoine Vermette took an offensive-zone holding penalty.

"It's nice," Kopitar said. "It's been too close too many times now that it's definitely nice to get the first one."

Kopitar also deftly slipped a pass to King off the right boards that King shot through an unsuspecting Smith for a 2-0 lead. Jordan Nolan made it 3-0 at 10:14 before King executed a perfect redirect of Robyn Regehr's point shot at 17:56 to give L.A. four goals on 14 shots.

It was the first time the Kings scored four goals in one period since March 5, 2013, against the St. Louis Blues.

"Our team put up seven goals," King said. "That's the first time since I've been here that we put up that big of a number. It went up and down tonight, obviously, with the big lead, giving it up. I think from 15 minutes left in the third, we got back to how we play."

Phoenix went more than 12 minutes in the first and second periods without a shot on goal, and its defense didn't give Smith much help with eight giveaways in the opening period.

"We went out and we took a penalty in the first shift in the offensive zone," Tippett said. "They scored. They got momentum and they ran with it. Put us behind the eight ball. We crawled back into it, and then we gave it away again."